The central spin model, as an exactly solvable model, has played a vital role in quantitatively understanding decoherence problem and entanglement dynamics [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
This model can be experimentally realized by superconductors [11]}, quantum dots [12]}, [13]}, [14]}, and nitrogen-vacancy centers in diamond [15]}.
Quantum battery problem can be naturally described in this model and we call it the “central-spin (quantum) battery”, where \(N_b\)  central spins serve as “battery cells” and \(N_c\)  bath spins serve as “charging units”, see Fig. REF .
However, research on the central-spin battery remains limited [16]}.
Assuming that only few photons in the view of the Holstein-Primakoff transformation, the central-spin battery will reduce to the Tavis-Cummings (TC) battery, which is a simplification of the Dicke battery.
The charging performance of the central-spin battery in this limit has been confirmed to have quantum advantage [16]}.
A recent Ref. [18]} pointed out that battery-charger entanglement is a major obstacle in work extraction by comparing the performance of a classical charger (coherent state) with that of nonclassical chargers (Fock and squeezed states) in the TC battery.
However, the correspondence between the central-spin battery and the TC battery breaks when the number of photons is far greater than the number of charging units.
